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%I #8 Nov 05 2020 07:25:51
%S 1,2,2,3,2,6,2,6,3,6,2,12,2,6,6,9,2,12,2,12,6,6,2,24,3,6,6,12,2,22,2,
%T 14,6,6,6,28,2,6,6,24,2,22,2,12,12,6,2,42,3,12,6,12,2,24,6,24,6,6,2,
%U 52,2,6,12,22,6,22,2,12,6,22,2,60,2,6,12,12,6,22,2,42
%N Dirichlet g.f.: Product_{k>=2} (1 + k^(-s))^2.
%C Dirichlet convolution of A045778 with itself.
%H Michael De Vlieger, <a href="/A328706/b328706.txt">Table of n, a(n) for n = 1..10000</a>
%H Jacob Sprittulla, <a href="https://arxiv.org/abs/2008.09984">On Colored Factorizations</a>, arXiv:2008.09984 [math.CO], 2020.
%F a(n) = Sum_{d|n} A045778(n/d) * A045778(d).
%t Block[{f}, f[m_, 1] := 1; f[1, n_] := 0; f[1, 1] := 1; f[0, n_] := 0; f[m_, n_] := f[m, n] = Total[f[# - 1, n/#] & /@ Select[Divisors[n], # <= m &]]; Table[DivisorSum[n, f[n/#, n/#]*f[#, #] &], {n, 80}]] (* _Michael De Vlieger_, Nov 04 2020 *)
%Y Cf. A045778, A301830.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Oct 26 2019
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